President Carter held an undisclosed meeting last December with Libya's charge d'affaires in Washington about three weeks after his brother, Billy, arranged an introductory meeting between natonal security adviser Zbigniew Brzezinski and the same Libyan.

When the White House issued a "white paper" Tuesday on its involvement in the Billy Carter-libya flap, press secretary Jody Powell indicated that there had been more than one contact involving Brzezinski and Ali Houderi, but said nothing about President Carter personally meeting the Libyan diplomat.

The previously unrevealed meeting between the president and Houderi took place after the Libyans had been asked to help win the release of American hostages in Iran, and after a mob in Tripoli had burned the American Embassy in the Libyan capital.

Early in the day yesterday, The Washington Post was told by several diplomatic sources that the president had met twice with Houderi. Early in the evening, Powell confirmed that Carter had met with Houderi once, but that he could find no record of a second meeting.

The White House never gave State Department officials prior notice on the sessions with Houderi, diplomatic sources told the Post. The State Department learned about the original Brzezinski-Billy Carter-Houderi meeting on Nov. 27 in cables from American diplomats in Tripoli, the sources said.

Powell, however, said he doubted that the State Department had not been informed. He quoted Brzezinski as saying he "feels sure that Secretary [of State Cyrus R.] Vance was informed of the Houderi meeting with the president and the one with Billy. He can't be sure if it was before or after the meetings took place."

There was no suggestion that Billy Carter's name or role came up in the president's meeting with Houderi in Washington last December, or that Billy Carter helped arrange it.

A month after the December meeting between the president and Houderi, Billy Carter received a check for $20,000, from the Libyan government. The check was conveyed by Houderi, the same diplomat with whom both Brzezinski and the president had met.

Under pressure from the Justice Department, Billy Carter registered last week as a Libyan agent, disclosed that he had received an additional check for $200,000 from Libya in April. Billy Carter said these payments were installments on what was to have been a $500,000 loan from Libya to him. The Justice Department declined to accept Carter's characterization of these payments as a loan.

Troubled by political criticism arising from Billy Carter's admission that he had received $220,000 from Libya, the White house over the past two days has tried to explain and justify its role. It issued a detailed statement Tuesday that revealed for the first time that Brzezinski had used Billy Carter as an intermediary to establish the White House's direct connection with the Libyans.

The White House statement made no mention of President Carter's personal dealings with Houderi, however.

State Department sources yesterday disputed the White House explanation for why Brzezinski turned to Billy Carter as an intermediary. In the Tuesday statement the White House said Brzezinski asked Billy Carter's help because of "the cool official relations then existing between the United States and Libya."

(Billy Carter's good relations with Libya were well-known at the time, and had already prompted a Justice Department investigation that was continuing when Brezezinski called on him.)

The State Department sources said it would have been easy to arrange a meeting with Houderi through normal diplomatic channels. They noted that David Newsom, the undersecretary of state for political affairs and a former ambassador to Libya, had a longstanding personal relationship with Houderi. States Deparment officials had been meeting with Houderi regularly since his arrival in Washington last September they said.

A White House official close to Brzezinski acknowledged yesterday that there were normal diplomatic channels available, but that Brzezinski wanted to meet Houderi personally "under the best possible circumstances." Apparently, Brzezinski thought the president's brother, because of his past ties with Libya, could help create such circumstances.

The White House explanation of who first suggested that Billy Carter set up a meeting changed yesterday. On Tuesday officials said the idea was Brzezinski's alone. Yesterday, Powell said, "Dr. Brzezinski cannot be sure exactly which person or persons may have mentioned the idea [of using Billy] to him first."

After Powell's briefing, a Brzezinski aide said it was possible that Billy Carter had set the idea in motion. "We just don't know," this aide said.

State Department officials had said Tuesday that they thought the whole idea came from Billy Carter.

According to an explanation offered last night by Powell, the Dec. 6 meeting involved President Carter, Brzezinski and Houderi. Powell said it grew out of a request by the Libyan to meet with the president's national security adviser. Houderi wanted to respond to the stiff rebuke he had received a day earlier at the State Department over the burning of the American Embassy in Tripoli on Dec. 2.

Brzezinski agreed to the meeting and told the president about it, Powell said. The president then asked to see the Libyan personally to express his own displeasure over the burning of the embassy. Carter spent 10 minutes with the envoy, Powell said.

The day before, Dec. 5, it had been publicly disclosed that leader Muammar Qaddafi had sent a personal plea to the Ayatollah Ruhollah Khomeini urging release of the American hostages. President Carter told Houderi on Dec. 6 that he appreciated this gesture, Powell said last night.

Authoritative sources said yesterday that if Vance got word of the meetings after the fact, he did not share it with others at the State Department.

One source said yesterday that the State Department still hadn't been given any official information about the meeting.

This lack of communication may have contributed to the different versions of the meetings provided by Powell and by diplomatic sources yesterday.The diplomatic sources said they understood that President Carter held two meetings with the Libyan envoy in December, while Powell said the Whtie House could find records of only one.

These meetings occurred at a period of high tension and drama for the United States and the entire Middle East region. Iranian militants had seized American hostages in November; later the same month mobs in Islamabad, Pakistan, burned the U.S. Embassy there; then the embassy in Libya was burned in early December.

The Carter edminstration was casting its diplomatic lines in all directions, looking for help to rescue the hostages and also trying to shore up America's shaky position in the region.

At the same time, tensions were high between Libya and America's principal Arab ally, Egypt. Diplomatic sources speculated that President Carter had to be very careful in his dealings with the Libyans not to give offense to Egyptian President Anwar Sadat. This might explain the secretiveness of the Carter-Houderi encounter, these sources speculated.

By coincidence, Houderi went to the State Department yesterday for a routine meeting.On the way to that session Houderi told a reporter that he had never met with President Carter, but "would like to." On the way out, however, when pressed as to whether he saw the president in December, Houderi said he would have "no comment."

Meanwhile, in a television interview yesterday, Billy Carter said he sought Vance's permission to arrange the meeting on Nov. 27 between Houderi and Brzezinski.

Having been under federal investigation for 18 months, Billy Carter said, "I knew the implcations of getting in between two governments." Therefore he called Vance to ask if he could play the intermediary role, he said.

Vance, however, said from his law office in New York: "I don't recall such a conversation." He added that "it is possible that I could have spoken with Mr. Carter on the phone and said that we would have no objection to his urging that the hostages be released."

That seemed to be a diplomatic but firm rebuttal of Billy Carter's version of events, since Vance omitted any mention of a discussion about setting up the Houderi meeting.

Last night CBS News reported that Billy Carter "in a roundabout way" had inquired about the status of C130 aircraft purchased by the Libyans but never delivered because of a U.S. embargo. Carter responded to that report by saying he had never discussed the aircraft problem with anyone in "the official government."